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 如果我們能夠將數學應用於真實環境中的日常生活問題，數學將變得更加重要和更有價值。這是因為解決問題是學習數學的重要目標之一。在生活中應用數學也可能有助於在處理現實生活中的問題時驗證並加強對數學概念的理解。但是，數學對於小學生而言很難，尤其是分數，因為抽象概念和缺乏與真實經驗的連結 。因此，為了在真實的學習環境下加強小學生的分數學習並研究他們的分數問題解決策略，我們設計並開發了基於平板電腦的應用程序Ubiquitous-Fraction（U-Fraction），讓學生在不論何時何地都可以學習分數。對於學習活動設計，給出了三個學習主題，例如基本分數概念和表示，分數簡化以及分數加法和減法。之後，要求學生解決分數符號問題和單詞問題，並分析他們的解決行為和策略經過了一次準實驗，結果顯示實驗組與對照組的學習成績存在顯著差異。進一步的數據分析發現，學生對分數的理解會嚴重影響分數問題的解決，例如正確的計算和正確的答案。關於分數解決問題策略的分析，將策略定義成三類，即優良、中等和不佳。事實證明，適度而良好的策略可以引導學生正確解決分數問題並獲得更好的學習成績。這是因為U-Fraction的反饋功能可以幫助學生創造性地，有效地開發解決分數問題的策略。最後，了解到學生對在真實環境中使用U-Fraction的看法，了解到非常正面和有趣。因此，強烈建議數學教師在真實情況下推廣和使用U-Fraction進行分數學習。
 Mathematics becomes more important and valuable if we can apply it to solve daily life problems in authentic contexts. This is because solving problems is one of the vital goals of learning mathematics. Applying mathematics in life can also possibly help to verify and consolidate mathematics concepts and understandings when dealing with problems in real life. However, it is quite difficult for elementary school students to study mathematics, especially fractions, due to abstract conception and lack of connecting authentic contexts. Therefore, to strengthen fraction learning of elementary school students with authentic contextual supports and investigate their fraction problem-solving strategies, we designed and developed a tablet-based application, Ubiquitous-Fraction(U-Fraction), and allowed students to learn fraction anywhere and anytime in the real world. Regarding learning activity design, three learning topics were given, such as basic fraction concepts and representation, fraction simplification, and fraction addition and subtraction. After that, students were asked to solve fraction symbolic problems and word problems and their solving behaviors and strategies were also analyzed.One quasi-experiment was conducted and the results showed that there were significant differences in learning achievements between the experiment group and the control group. Further data analysis found that students' fraction understanding can significantly affect fraction problem solving like correct calculation and correct answer. Regarding the analysis of fraction problem-solving strategies, three categories of strategies will be defined, namely bad, moderate, and good. Moderate and good strategies were demonstrated to lead students to solve fraction problems correctly and obtain better learning achievements. This is because the feedback feature of U-Fraction can help students to develop fraction problems solving strategies creatively and effectively. Finally, students' perceptions toward using U-Fraction in authentic contexts were studied and found very positive and playful. Therefore, it is strongly suggested for mathematic teachers to promote and use U-Fraction for fraction learning in authentic contexts.
 Abstract i中 文 摘 要 iiAcknowledgment iiiList of Content ivList of Table viList of Figure viiChapter 1 Introduction 11.1. Background and Motivation 11.2. Purpose of the Study 3Chapter 2 Literature Review 42.1. Fraction learning in Elementary School and the Difficulties 42.2. Fraction learning in Authentic Contexts 52.3. Students’ Strategy to Solve the Problems 72.4. Motivation Questionnaire and Technology Acceptance Model (TAM) 9Chapter 3 System Design and Implementation 113.1. Ubiquitous Fraction (U-Fraction) System 113.1.1. Activity Section 123.1.2. Direction Section 153.1.3. FRT in Fraction Representation Option 183.1.4. FSP Tasks and FWP Tasks in Problem Solving Option 203.2. Automatic Feedback 23Chapter 4 Research Method 254.1. Participants and Subject 254.2. Research Flow 254.3. Experimental Procedure 264.4. Research Architecture 284.5. Learning Tasks 364.6. Data Analysis 39Chapter 5 Result and Analysis 415.1. Learning Achievement between the Two Groups 415.2. Learning Tasks between the Two Groups 445.3. Learning Behavior using U-Fraction with Authentic Contexts 475.4. The Most Important Predictor Learning Behavior for Learning Achievement 495.5. Type of Strategy in Problem Types and Posttest Types 505.6. Learning Motivation 535.7. Students’ Perception toward Using U-Fraction 54Chapter 6 Conclusions 576.1. Conclusions 576.2. Limitations 586.3. Future Study 59References 60Appendix 1 MSLQ Questionnaire 65Appendix 2 TAM Questionnaire 69Appendix 3 Pretest 71Appendix 4 Posttest 78